Derive and interpret four performance measures for a property-casualty insurer: the loss, expense, combined and operating ratios.

FRM® Part I · Financial Markets and Products · Insurance Companies and Pension Plans · FRM1.FM.2.f

The idea

Four ratios judge a property-casualty insurer, all expressed as a percentage of premiums. Loss ratio = claims losses ÷ premiums. Expense ratio = operating and acquisition expenses ÷ premiums. Combined ratio = loss ratio + expense ratio. Some versions also add policyholder dividends. A combined ratio above 100 percent means an underwriting loss before investment income. Operating ratio = combined ratio − investment income ratio. The investment income ratio is investment income expressed as a percentage of premiums, so an insurer can lose money on underwriting yet still be profitable overall. Remember that if premiums fall while claims and fixed expenses stay the same, the loss ratio and the expense ratio both rise, because premiums are the denominator. The classic exam trap is subtracting investment income to reach the combined ratio, or adding it to reach the operating ratio.

Formulas

Loss ratio

LR = L ÷ P

L: claims losses
P: premiums

A percentage of premiums. Premiums are the denominator, so a fall in premiums with unchanged claims raises the ratio.

Combined ratio

CR = (L + E) ÷ P

L: claims losses
E: operating and acquisition expenses
P: premiums

Above 100% is an underwriting loss. Do not subtract investment income here; that belongs in the operating ratio.

Operating ratio

OpR = CR − I ÷ P

CR: the combined ratio
I: investment income
P: premiums

Investment income is subtracted, never added. Below 100% means profitable overall even if underwriting loses money.

A practice question

From the question bank, with the reason each wrong option is wrong.

For a property-casualty insurer, the loss ratio is calculated as:

operating and acquisition expenses divided by premiumsWhy not: This is the expense ratio.
claims losses divided by premiums - correct
claims losses divided by total assetsWhy not: The denominator should be premiums, not assets, for the loss ratio.
claims losses plus expenses minus investment income, divided by premiumsWhy not: This is the operating ratio, which also includes investment income.

Loss ratio = losses from claims / premiums. Adding the expense ratio gives the combined ratio, and subtracting the investment income ratio gives the operating ratio.

A harder one

A property-casualty insurer reports premiums of USD 800 million, claims losses of USD 560 million, expenses of USD 224 million and investment income of USD 56 million. The combined ratio is closest to:

98% - correct
70%Why not: This is the loss ratio only; expenses must also be included.
91%Why not: This subtracts investment income, which gives the operating ratio, not the combined ratio.
105%Why not: Adds investment income instead of leaving it out; investment income is not a cost.

Loss ratio = 560/800 = 70%; expense ratio = 224/800 = 28%; combined = 98%. The operating ratio would be 98% - 7% = 91%.

The hardest tier

An insurer has a loss ratio of 68% and an expense ratio of 28% on premiums of USD 500 million. To win market share it cuts its prices by 10% for the same exposure, so premiums fall to USD 450 million, while claims losses and expenses in USD stay the same. The new combined ratio is closest to:

103.6%Why not: Adjusts the loss ratio for the price cut but leaves the expense ratio at 28%, though expenses are also now spread over smaller premiums.
106.7% - correct
96.0%Why not: Assumes the ratios are unchanged; they rise because premiums, the denominator, have fallen.
86.4%Why not: Multiplies by 0.9 instead of dividing; a lower premium raises, not lowers, the ratios.

Claims + expenses = 96% x 500 = USD 480 million. New combined = 480 / 450 = 106.7%. A price cut raises every ratio that uses premiums as the denominator.

In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.

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